Solve for $x$ and $y$ using elimination. ${4x+y = 21}$ ${3x-y = 7}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $7x = 28$ $\dfrac{7x}{{7}} = \dfrac{28}{{7}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {4x+y = 21}\thinspace$ to find $y$ ${4}{(4)}{ + y = 21}$ $16+y = 21$ $16{-16} + y = 21{-16}$ ${y = 5}$ You can also plug ${x = 4}$ into $\thinspace {3x-y = 7}\thinspace$ and get the same answer for $y$ : ${3}{(4)}{ - y = 7}$ ${y = 5}$